Optimal Portfolio Strategy Research Articles

Portfolio Selection under Median and Quantile Maximization

Although maximizing median and quantiles is intuitively appealing and has an axiomatic foundation, it is difficult to study the optimal portfolio strategy due to the discontinuity and time inconsistency in the objective function. We use the intra-personal equilibrium approach to study the problem. Interestingly, we find that the only viable outcome is from the median maximization, because for other quantiles either the equilibrium does not exist or there is no investment in the risky assets. The median maximization strategy gives a simple explanation to why wealthier people invest more percentage of their wealth in risky assets.

Mean-Variance Portfolio Selection with Tracking Error Penalization

This paper studies a variation of the continuous-time mean-variance portfolio selection where a tracking-error penalization is added to the mean-variance criterion. The tracking error term penalizes the distance between the allocation controls and a reference portfolio with same wealth and fixed weights. Such consideration is motivated as follows: (i) On the one hand, it is a way to robustify the mean-variance allocation in case of misspecified parameters, by “fitting” it to a reference portfolio that can be agnostic to market parameters; (ii) On the other hand, it is a procedure to track a benchmark and improve the Sharpe ratio of the resulting portfolio by considering a mean-variance criterion in the objective function. This problem is formulated as a McKean-Vlasov control problem. We provide explicit solutions for the optimal portfolio strategy and asymptotic expansions of the portfolio strategy and efficient frontier for small values of the tracking error parameter. Finally, we compare the Sharpe ratios obtained by the standard mean-variance allocation and the penalized one for four different reference portfolios: equal-weights, minimum-variance, equal risk contributions and shrinking portfolio. This comparison is done on a simulated misspecified model, and on a backtest performed with historical data. Our results show that in most cases, the penalized portfolio outperforms in terms of Sharpe ratio both the standard mean-variance and the reference portfolio.

A Behavioral Portfolio Model with Interval Return and Investor’s Sentiment

This paper proposes a behavioral portfolio decision model with interval returns and investor’s sentiment. A sentiment-adjusted mean model for behavioral portfolio selection is presented by taking into account investor’s sentiment return and multiple mental accounts. The proposed behavioral model maximizes the sentimental mean value of portfolio interval return and ensures the portfolio interval return of each mental account exceeding the given minimum return level with a given possibility degree. Then, multiple programming models are designed to solve the optimal behavioral portfolio strategy. Finally, a numerical example is given to illustrate the validity of the proposed approach.

Stopping the Clock On Retirement: Target Wealth Stopping Time Problems

A common approach to retirement planning focuses on building sufficient funds to retire at a fixed, predefined retirement time horizon. Optimal portfolio strategies are applied in an effort to achieve this goal. These strategies typically lead to the wealth at retirement having substantial uncertainty, making it difficult for investors to understand how much to save and how the savings rate impacts their wealth when they retire. A cash investment overcomes these problems, but is generally too expensive for most savers. Instead, we optimize on statistics of the stopping time at which one has achieved a target wealth. This is related to the notion of labor optionality introduced in Labor supply flexibility and portfolio choice in a life cycle model, 1992, by Bodie, Merton, and Samuelson, and avoids some of the shortcomings of predefined retirement time approaches. We solve this retirement stopping time problem using stochastic optimization with a Markov control. The objective function is relatively flat near the optimum, so, for example, reducing both variance and trading frequency have little impact on the optimum. We also prove that shorting strategies are stochastically dominated by ones which do not short, which is of general interest for financial optimization problems.

BAYESIAN LEARNING FOR THE MARKOWITZ PORTFOLIO SELECTION PROBLEM

We study the Markowitz portfolio selection problem with unknown drift vector in the multi-dimensional framework. The prior belief on the uncertain expected rate of return is modeled by an arbitrary probability law, and a Bayesian approach from filtering theory is used to learn the posterior distribution about the drift given the observed market data of the assets. The Bayesian Markowitz problem is then embedded into an auxiliary standard control problem that we characterize by a dynamic programming method and prove the existence and uniqueness of a smooth solution to the related semi-linear partial differential equation (PDE). The optimal Markowitz portfolio strategy is explicitly computed in the case of a Gaussian prior distribution. Finally, we measure the quantitative impact of learning, updating the strategy from observed data, compared to nonlearning, using a constant drift in an uncertain context, and analyze the sensitivity of the value of information with respect to various relevant parameters of our model.

Finite horizon portfolio selection problems with stochastic borrowing constraints

<p style='text-indent:20px;'>In this paper we investigate the optimal consumption and investment problem with stochastic borrowing constraints for a finitely lived agent. To be specific, she faces a credit limit which is a constant fraction of the present value of her stochastic labor income at each time. By using the martingale approach and transformation into an infinite series of optimal stopping problems which has the same characteristic as finding the optimal exercise time of an American option. We recover the value function by establishing a duality relationship and obtain the integral equation representation solution for the optimal consumption and portfolio strategies. Moreover, we provide some numerical illustrations for optimal consumption and investment policies.

Exploring the Moral Hazard Evolutionary Mechanism for BIM Implementation in an Integrated Project Team

Integrated project delivery (IPD) is a new emerging delivery system, contributes to increase value to the owner, reduces waste and maximizes efficiency in the life cycle of projects. However, IPD system has not yet shifted from pilot-alike or particular-purposed cases to large-scale applications. The huge advantages of building information modeling (BIM) are far from being exploited, which directly leads to the delivered outcomes below expectations, thereby causing obstacles to widespread application of IPD system. The reasons impeding the successful application of BIM has been a hot topic. Previous studies suggested that moral hazard behavior is a critical inducer leading to the undesirable outcomes. However, very few studies have studied the evolution mechanism of moral hazard behavior for BIM application. To fill this knowledge gap, this study proposed a novel model, aiming to capture dynamically the interactive behavior of BIM-based strategy selections using evolutionary game theory. Five parameters of monitoring cost, proprietary cost, incentive payment, punishment and speculative benefit are extracted and defined in the proposed model. Numerical simulations are conducted with MATLAB 2016a. The simulation results showed that when incentive payment is higher than the sum of speculative benefit and proprietary cost, interactive behavior of both game players will move toward the optimal portfolio strategy. Incentive payment and punishment have negative correlations with the probability of moral hazard behavior for BIM application. Parameters of speculative benefit and proprietary cost affect positively implementation probability of moral hazard behavior of employing BIM. This study can provide theoretical and managerial implications for integrated project managers and related government department to improve implementation of BIM and IPD system, and also contribute to its sustainable development.

Risk-Based Portfolio Optimization in the Cryptocurrency World

This study explores the performance of seven state-of-the-art risk-based portfolio optimization strategies from the perspective of a cryptocurrency investor. Analyzing the inverse volatility, minimum variance, l2-norm constrained minimum variance, l2-norm constrained maximum decorrelation, maximum diversification and risk parity portfolio, we find that most strategies systematically outperform individual cryptocurrencies and the equally-weighted benchmark portfolio. Further, a bull and bear market performance comparison as well as tail, extreme risk, and diversification analyses reveal that these strategies provide significant downside risk reduction. The results are robust to using different estimation windows, rebalancing periods and covariance estimation methodologies. Finally, our empirical results indicate that the maximum decorrelation portfolio is the worst strategy in terms of risk-adjusted return, while the long-only minimum variance portfolio is the best performing strategy.

The Kelly Growth Optimal Portfolio with Ensemble Learning

As a competitive alternative to the Markowitz mean-variance portfolio, the Kelly growth optimal portfolio has drawn sufficient attention in investment science. While the growth optimal portfolio is theoretically guaranteed to dominate any other portfolio with probability 1 in the long run, it practically tends to be highly risky in the short term. Moreover, empirical analysis and performance enhancement studies under practical settings are surprisingly short. In particular, how to handle the challenging but realistic condition with insufficient training data has barely been investigated. In order to fill voids, especially grappling with the difficulty from small samples, in this paper, we propose a growth optimal portfolio strategy equipped with ensemble learning. We synergically leverage the bootstrap aggregating algorithm and the random subspace method into portfolio construction to mitigate estimation error. We analyze the behavior and hyperparameter selection of the proposed strategy by simulation, and then corroborate its effectiveness by comparing its out-of-sample performance with those of 10 competing strategies on four datasets. Experimental results lucidly confirm that the new strategy has superiority in extensive evaluation criteria.

Uncertain portfolio optimization problem under a minimax risk measure

• A new uncertain risk measure is defined for the modeling of investment risk. • An uncertain portfolio optimization model is formulated. • A method is presented for finding the set of analytic Pareto optimal solutions . Portfolio optimization problem is concerned with choosing an optimal portfolio strategy that can strike a balance between maximizing investment return and minimizing investment risk. In many cases, the return rate of risky asset is neither a random variable nor a fuzzy variable. Then, it can be described as an uncertain variable. But, the existing works on uncertain portfolio optimization problem fail to find an analytic solution of optimal portfolio strategy. In this paper, we define a new uncertain risk measure for the modeling of investment risk. Then, an uncertain portfolio optimization model is formulated. By introducing a new variable, we transform it into an equivalent bi-criteria optimization model. Then, we derive a method for the construction of the set of analytic Pareto optimal solutions. Finally, a numerical simulation is carried out to show the applicability of the proposed model and the convenience of finding the analytic solution.

Portfolio optimization based on empirical mode decomposition

The investigation about the cross-correlation among financial assets has drawn broad attention recently. Due to the nonlinear and non-stationary identities of the financial time series, e.g., stock return time series, the cross-correlation for different level of fluctuations are quite important for both academia and financial practitioners. Here we use the empirical mode decomposition (EMD) method to analyze the cross-correlation structure among different level of fluctuations for financial assets. The correlation-based networks are then employed to determine the clustering property of stock market. We then propose several portfolio optimization strategies based on the EMD correlation-based networks. Using the topological information of the networks, we can construct some portfolios with high return and low risk. Under two portfolio evaluation frameworks, we prove that these portfolios have consistently good performance.

Worst-case portfolio optimization in discrete time

We consider discrete-time portfolio problems of an investor when taking the possibility of market crashes into account. In the case of the logarithmic utility function, we construct the worst-case optimal portfolio strategy by an indifference principle. Then, we extend the setting to general utility functions and derive the worst-case optimal portfolio processes via the characterization by a dynamic programming equation. Furthermore, we numerically examine the convergence behavior of the discrete-time worst-case optimal portfolio processes for the choice of popular utility functions when the time between two possible price changes tends to zero.

Portfolio selection based on semivariance and distance correlation under minimum variance framework

In the minimum variance model, the covariance matrix plays an important role because it measures the risk and relationship of asset returns simultaneously under the normality assumption. However, in practice, the distribution of asset returns is nonnormal and has an obvious fat‐tail nature. In addition, the risk is one‐sided. In this paper, the main objective is to propose a better tool to replace the covariance matrix. The covariance matrix can be decomposed into two parts: a diagonal variance matrix and a square matrix with its elements being the Pearson correlation coefficient. A substitution of the covariance matrix is presented by replacing the variance and Pearson correlation coefficient in the decomposition of the covariance matrix with a semivariance and distance correlation coefficient, respectively. The proposed portfolio optimization strategy is applied to empirical data, and the numerical studies show the strategy performs well.

Finite horizon portfolio selection with a negative wealth constraint

This paper studies an optimal consumption and portfolio strategy with a negative wealth constraint for a finitely-lived economic agent. That is, we allow the individual agent to borrow partially against her/his future labor income during a finite time horizon. We derive the associated Hamilton–Jacobi–Bellman equation and use the Mellin transform to obtain the integral equation representation satisfied by the free boundary. Moreover, we derive an analytic representation for the optimal consumption, wealth, and portfolio, and provide some numerical implications for the optimal strategies.

A copula-based scenario tree generation algorithm for multiperiod portfolio selection problems

Global financial investors have been confronted in recent years with an increasing frequency of market shocks and returns’ outliers, until the unprecedented surge of financial risk observed in 2008. From a statistical viewpoint, those market dynamics have shown not only asymmetric returns and fat tails but also a time-varying tail dependence, stimulating the formulation of portfolio selection models based on such assumptions. The concept of tail dependence on upper or lower tails, roughly speaking, focuses on the risk that tail events may occur jointly in different markets. This notion can be given a rigorous probabilistic definition, and it turns out that a distinction between upper and lower tails is relevant in portfolio management. In this paper, relying on a discrete modeling framework, we present a scenario generation algorithm able to capture this time-varying asymmetric tail dependence, and evaluate resulting optimal investment policies based on 4-stages 1-month planning horizons. The scenario tree aims at approximating a stochastic process combining an ARMA-GARCH model and a dynamic Student-t-Clayton copula. From a methodological viewpoint, scenario trees are generated from this model by stage-wisely sampling and clustering and to improve tail fitting with original data, the scenarios’ nodal probabilities are calibrated on the returns’ lower tails for a set of equity indices. The resulting scenario trees are then applied to solve a multiperiod portfolio selection problem. We present a set of empirical results to validate the adopted statistical approach and the optimal portfolio strategies able to capture asymmetric tail returns.

Practical Applications of Portfolio Optimization Strategy for Concentrated Portfolios: Models and Time Horizons

<h3>Practical Applications Summary</h3> In <b>Portfolio Optimization Strategy for Concentrated Portfolios: <i>Models and Time Horizons</i></b>, from the Fall 2018 issue of <b><i>The Journal of Wealth Management</i></b>, authors <b>Sarah Campbell</b>, <b>James Chong</b>, <b>William Jennings</b>, and <b>G. Michael Phillips</b> (all of <b>MacroRisk Analytics</b>) examine the relative merits of portfolio-construction approaches for concentrated, or high-conviction, (i.e., 15 or fewer holdings) portfolios. The authors’ study in part stems from the debate over the efficacy of an optimization approach to portfolio construction compared with an equally weighted (or “naïve”) approach. The authors’ intention is to help guide wealth managers in choosing a portfolio-optimization method best suited to their investment priorities (e.g., maximizing returns, minimizing risk, balancing risk and returns). The authors apply a Monte Carlo simulation to generate 18,000 buylists of stocks. From each buylist, the simulation derives an optimized portfolio and two equally weighted portfolios: one of stocks selected through optimization (a “hybrid” portfolio) and the other of randomly selected stocks (a “benchmark” portfolio). The study calculates each portfolio’s forward average yearly returns, annual standard deviations, and forward risk–return ratios for several different time frames, and then compares relative performance. The authors emphasize the importance of choosing the suitable portfolio-construction approach: one aligned with the number of holdings in a portfolio and investment horizon or one that best performs under the distinct circumstances faced by the wealth manager. <b>TOPICS:</b>Portfolio construction, analysis of individual factors/risk premia, tail risks, performance measurement

Portfolio Optimization for a Large Investor Controlling Market Sentiment Under Partial Information

We study a portfolio optimization problem for an investor whose actions have an indirect impact on prices. We consider a market model with a risky asset price process following a pure-jump dynamics with an intensity modulated by an unobservable continuous-time finite-state Markov regime-switching process. We assume that decisions of the investor affect the generator of the regime-switching process which results in an indirect impact on the price process. Using filtering theory, we reduce this problem with partial information to one with full information and solve it for logarithmic and power utility preferences. In particular, we apply control theory for piecewise deterministic Markov processes to derive the optimality equation. Finally, we provide an example with a two-state Markov regime-switching process and discuss how an investor's ability to control the intensity of it affects optimal portfolio strategies as well as the optimal wealth under full and partial information.

Portfolio Optimization under Correlation Constraint

We consider the problem of portfolio optimization with a correlation constraint. The framework is the multiperiod stochastic financial market setting with one tradable stock, stochastic income and a non-tradable index. The correlation constraint is imposed on the portfolio and the non-tradable index at some benchmark time horizon. The goal is to maximize portofolio's expected exponential utility subject to the correlation constraint. Two types of optimal portfolio strategies are considered: the subgame perfect and the precommitment ones. We find analytical expressions for the constrained subgame perfect (CSGP) and the constrained precommitment (CPC) portfolio strategies. Both these portfolio strategies yield significantly lower risk when compared to the unconstrained setting, at the cost of a small utility loss. The performance of the CSGP and CPC portfolio strategies is similar.

Tail Behavior in Portfolio Optimization for Equity Style Factors

Diversification has been long considered an essential part of investing for the long term. Our paper aims to look further on portfolio diversification and how asset allocation can be optimized. We suggest that the selection of investments in a portfolio should be based on how the market behaves subject to extreme events or in other words on tail behavior. Firstly, we look at equity style factors and how they perform in the worst 10 scenarios of the market. Second, we regress ETF factor-based indices on these style factors and evaluate how much of the indices’ performance can be explained. We then construct a hypothetical portfolio and suggest a portfolio optimization strategy which takes into consideration how its assets are behaving in bad times of the market economy. Our results indicate that style factors offer diversification benefits during distress periods. As a consequence, they comprise a useful source of information when we wish to optimize the asset allocation of our portfolio.

(Almost) Model‐Free Recovery

ABSTRACTUnder mild assumptions, we recover the model‐free conditional minimum variance projection of the pricing kernel on various tradeable realized moments of market returns. Recovered conditional moments predict future realizations and give insight into the cyclicality of equity premia, variance risk premia, and the highest attainable Sharpe ratios under the minimum variance probability. The pricing kernel projections are often U‐shaped and give rise to optimal conditional portfolio strategies with plausible market timing properties, moderate countercyclical exposures to higher realized moments, and favorable out‐of‐sample Sharpe ratios.